69 research outputs found
Consistent Valuation Across Curves Using Pricing Kernels
The general problem of asset pricing when the discount rate differs from the
rate at which an asset's cash flows accrue is considered. A pricing kernel
framework is used to model an economy that is segmented into distinct markets,
each identified by a yield curve having its own market, credit and liquidity
risk characteristics. The proposed framework precludes arbitrage within each
market, while the definition of a curve-conversion factor process links all
markets in a consistent arbitrage-free manner. A pricing formula is then
derived, referred to as the across-curve pricing formula, which enables
consistent valuation and hedging of financial instruments across curves (and
markets). As a natural application, a consistent multi-curve framework is
formulated for emerging and developed inter-bank swap markets, which highlights
an important dual feature of the curve-conversion factor process. Given this
multi-curve framework, existing multi-curve approaches based on HJM and
rational pricing kernel models are recovered, reviewed and generalised, and
single-curve models extended. In another application, inflation-linked,
currency-based, and fixed-income hybrid securities are shown to be consistently
valued using the across-curve valuation method.Comment: 56 page
Information, Inflation, and Interest
We propose a class of discrete-time stochastic models for the pricing of
inflation-linked assets. The paper begins with an axiomatic scheme for asset
pricing and interest rate theory in a discrete-time setting. The first axiom
introduces a "risk-free" asset, and the second axiom determines the
intertemporal pricing relations that hold for dividend-paying assets. The
nominal and real pricing kernels, in terms of which the price index can be
expressed, are then modelled by introducing a Sidrauski-type utility function
depending on (a) the aggregate rate of consumption, and (b) the aggregate rate
of real liquidity benefit conferred by the money supply. Consumption and money
supply policies are chosen such that the expected joint utility obtained over a
specified time horizon is maximised subject to a budget constraint that takes
into account the "value" of the liquidity benefit associated with the money
supply. For any choice of the bivariate utility function, the resulting model
determines a relation between the rate of consumption, the price level, and the
money supply. The model also produces explicit expressions for the real and
nominal pricing kernels, and hence establishes a basis for the valuation of
inflation-linked securities
Pricing Fixed-Income Securities in an Information-Based Framework
In this paper we introduce a class of information-based models for the
pricing of fixed-income securities. We consider a set of continuous- time
information processes that describe the flow of information about market
factors in a monetary economy. The nominal pricing kernel is at any given time
assumed to be given by a function of the values of information processes at
that time. By use of a change-of-measure technique we derive explicit
expressions for the price processes of nominal discount bonds, and deduce the
associated dynamics of the short rate of interest and the market price of risk.
The interest rate positivity condition is expressed as a differential
inequality. We proceed to the modelling of the price-level, which at any given
time is also taken to be a function of the values of the information processes
at that time. A simple model for a stochastic monetary economy is introduced in
which the prices of nominal discount bonds and inflation-linked notes can be
expressed in terms of aggregate consumption and the liquidity benefit generated
by the money supply
Discrete-Time Interest Rate Modelling
This paper presents an axiomatic scheme for interest rate models in discrete
time. We take a pricing kernel approach, which builds in the arbitrage-free
property and provides a link to equilibrium economics. We require that the
pricing kernel be consistent with a pair of axioms, one giving the
inter-temporal relations for dividend-paying assets, and the other ensuring the
existence of a money-market asset. We show that the existence of a
positive-return asset implies the existence of a previsible money-market
account. A general expression for the price process of a limited-liability
asset is derived. This expression includes two terms, one being the discounted
risk-adjusted value of the dividend stream, the other characterising retained
earnings. The vanishing of the latter is given by a transversality condition.
We show (under the assumed axioms) that, in the case of a limited-liability
asset with no permanently-retained earnings, the price process is given by the
ratio of a pair of potentials. Explicit examples of discrete-time models are
provided
Securities Pricing with Information-Sensitive Discounting
In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particu- lar we consider credit-risky assets that may include random recovery upon default. The market filtration is generated by a collection of information processes associated with economic factors, on which in- terest rates depend, and information processes associated with mar- ket factors used to model the cash flows of the securities. We use information-sensitive pricing kernels to give rise to stochastic interest rates. Semi-analytical expressions for the price of credit-risky bonds are derived, and a number of recovery models are constructed which take into account the perceived state of the economy at the time of default. The price of European-style call bond options is deduced, and it is shown how examples of hybrid securities, like inflation-linked credit-risky bonds, can be valued. Finally, a cumulative information process is employed to develop pricing kernels that respond to the amount of aggregate debt of an economy.Asset pricing, incomplete information, stochastic interest rates, credit risk, recovery models, credit-inflation hybrid securities, information-sensitive pricing kernels
Pricing Fixed-Income Securities in an Information-Based Framework
In this paper we introduce a class of information-based models for the pricing of fixed-income securities. We consider a set of continuous- time information processes that describe the flow of information about market factors in a monetary economy. The nominal pricing kernel is at any given time assumed to be given by a function of the values of information processes at that time. By use of a change-of-measure technique we derive explicit expressions for the price processes of nom- inal discount bonds, and deduce the associated dynamics of the short rate of interest and the market price of risk. The interest rate positiv- ity condition is expressed as a differential inequality. We proceed to the modelling of the price-level, which at any given time is also taken to be a function of the values of the information processes at that time. A simple model for a stochastic monetary economy is introduced in which the prices of nominal discount bonds and inflation-linked notes can be expressed in terms of aggregate consumption and the liquidity benefit generated by the money supply.Fixed-income securities, interest rate theory, inflation, inflation-linked securities, non-linear filtering, incomplete information
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